For the case Example REF , setting \(m = 2000\) , \(n = 500\) , \(r = 100\) , \(a = 1\) , \(b = 1000\)  and \(\kappa = 1\) , then we generate the low rank matrix \(A\)  by Eq.(REF ). For practical applications in not too large datasets, setting \(p\)  as shown in Algorithm REF  is rather time consuming. Followed by the work in [1]}, [2]}, [3]}, setting the parameter \(p = 100\) , then we make a comparison between SVD algorithm and our QiSLS algorithm with different parameters \(k\) . The statistical leverage score results of Algorithm REF  with different parameters \(k\)  are shown in Figure REF . In Figure REF , Similar as the Example REF , the red dashed line and black dot denote the results of statistical leverage scores \(\ell _{i}\)  and \(\tilde{\ell }_{i}\) , respectively. Comparing with the parameters \(k = 75\)  and \(k = 82\) , when \(k = 88\) , except that the two ends (the small and large parts), the remaining parts are well approximated. Without loss of generality, we find that with the increasing properly parameter \(k\) , the QiSLS algorithm can return a better approximation on SLS \(\ell _{i}\) .
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